SYSU Professor Zhu Xiping Solved One-year-old Math Mystery

 

Ponicare Conjecture, one of the most famous open problems in mathematics and has been around for about one hundred years, has been completely solved by scientists recently. Renowned mathematician Qiu Chentong, a Harvard professor and Fields prize winner, announced in CAS Chenxing Math Center on June 3 that Professor Zhu Xiping with Sun Yat-sen University and Professor Cao Huaidong with Lehigh University in Pennsylvania had produced a complete proof to the conjecture on basis of research achievements by preceding American and Russian scientists.

“This can be compared to the construction of a building. The forerunners have laid the foundation, while the last phase work, “topping out”, is completed by the Chinese,” said Qiu Chentong. “It’s an extraordinary accomplishment, much more important than Goldbach Conjecture.”

“This is the first time that a complete solution to the problem had been published on an international math journal, which is a very great achievement”, said mathematician Yang Yue.

"A Complete Proof of the Poincare and Geometrization Conjectures - application of the Hamilton-Perelman theory of the Ricci flow", a 300-plus-page paper co-authored by professor Zhu and professor Cao, has been published in the June issue of the U.S.-based Asian Journal of Mathematics.

Rated as one of the world’s seven toughest problems, Poincaré Conjecture was first presented by the French mathematician Henri Poincaré in 1904. In technical terms the conjecture states that if a space is homotopically equivalent to a three-dimensional sphere it is homeomorphic to the three-sphere. In less technical terms it says that if you have a bounded three-dimensional space in which all loops can be shrunk down to points, it has to be the three-sphere. In May 2000, Us-based Clay Mathematics Institute, a private organization, had established a $7 million prize fund, $1 million each for the solution of these seven famous mathematical problems.

For more than 100 years, numerous mathematicians around the world have been seeking solutions to the Poincaré Conjecture. In the early 1980s, U.S. mathematician William P. Thurston had produced partial proof of Poincar's Conjecture on geometric structure, and was awarded the Fields Prize for the achievement. Fellow American Richard Hamilton completed the majority of the program and the geometrization conjecture. In 2003, Russian mathematician Grigory Perelman made key new contributions.

Availing of their research findings, Zhu and Cao, for the first time, successfully worked out the “singularity point”problem of this conjecture and came up with a complete proof of the conjecture.

From September last year to March this year, this pair have been invited to Harvard to give lectures about their research to five Harvard professors including the dean of the Math Department and answer their questions.

Qiu pointed out that their work would help scientists to further understand three-dimensional space and greatly influence the development of physics and engineering.

2006.6.3